solve-each-equation-for-x-a2x-53-quad-text-b-ln-xln-x-11

Question

Solve each equation for $x$ .

$$(a)2^{x-5}=3 \quad 	ext { (b) } \ln x+\ln (x-1)=1$$

Amrita Bhasin · Accepted Answer

this question asks us to solve each equation for Axe. Let&#x27;s take the log of both sides of the base too, so we can cancel off the two on the left hand side. Leaving us with acts is five close long to the base, two of three for part B. We&#x27;re following a similar route. We know this is essentially natural. Log of X minus one. Writing this and factored form naturally, Axe times X minus one is a corpulent to natural log of E which gives us ax squared minus acts minus. He is equivalent to zero. We know that if we&#x27;re using the core jack formula, we can write this as one plus squirt of one plus for E divided by two, or you can leave it as the fraction.

Amrita Bhasin · Answer

rewriting this equation. Exponential form As the Cube drew off five X minus three equals E squared, multiplying both sides by the power of three. To get rid of the Cube drew on the left hand side, we know that we now have five X minus three equals eat of the two e squared to the third Power is eating the sex, which gives us five acts, equals eat. The sex plus three acts equals eight of the sex plus three over five. And if use a calculator for this, you&#x27;ll discover that 81.2858 equals acts.

Eric Solomon · Answer

Let&#x27;s solve the equation. The natural log of X squared plus one equals five. So the first step we can do here is simply move this +11 of the right hand side by subtracting one from both sides. Make it the natural log of X squared equals four. We can only also use the property that the natural log of X to some power, eh? For a lot of you can actually pull that a out into the friend and we would get a times the natural. Lagerback&#x27;s so applying that here we can write the Ellen of Expert as to terms the natural log of X that&#x27;s gonna equal for invaluable sides by two. Can we get the Ln of X equals two? And if I next we want to raise both sides, um, to the power we&#x27;re gonna take e and raise them. We&#x27;re gonna take E and we&#x27;re gonna raise the west side. So, you know, the next time again, he&#x27;s square. But he did. The Ellen of X is simply X and he squared. Using a calculator is roughly 7.39 So we get that as our value for X. That solves the equation

Heather Zimmers · Answer

all right. We want to take our lager with Mickey Equation, and we want to change it to exponential form in order to solve it. And remember that when you see natural log, it means long based E. So we have law based E g of X squared minus one equals three. So changing that into its exponential form, we will have the base e raised to the power three equals X squared minus one. Now let&#x27;s sell that for X so we can add one to both sides and we get e cubed. Plus one equals X squared. And then we can square root both sides and we get plus or minus the square root of E cubed plus one equals X and after party. I don&#x27;t know about you, but when I look at this, I see a quadratic type situation. I think it looks a lot like quadratic equations that we would solve by factoring. So let&#x27;s factor this into to buy no meals. To get each of the two X, you would multiply E to the X by each of the X. Remember the exponents property? You would add those powers. X plus X is two X and for the last to get to. We could do minus two and minus one and notice if you foil that, you get minus three e to the X in the inside and the outside added together. So now we&#x27;ll take each of these factors and will set them equal to zero. Each of the X minus two equals zero or e to the X minus. One equals zero for the 1st 1 Add two to both sides and for the 2nd 1 add one to both sides. Okay. Now, to solve these, we&#x27;re going to need to take the natural log of both sides and we get X equals Natural log of to or X equals natural log of one natural log of one is just zero. So we have X equals natural log of to or X equal zero

Himanshu Kushwaha · Answer

well. Look off three X plus five minus one is required along off to X minus terry This Can Britain as look off three X plus five minus log off is required. Look off to X minus three. Now we use the property here looking minus log and is equal to look everywhere by envy. Get logo three X Plus five, divided by E, is required to look off to X minus. Study by comparing the local sex. Forget three x plus five. Divided by is equal to X minus three. From your vigor Terry X plus five. It will go to X minus three e Now if we subtract three x from both sides. Nte boto Side bigot three Ive plus five is equal to e X minus three. X bigot X multiplied by two e minus three is equal to three e plus five. From here, bigot X is equal to three e plus five. Whereby toe E minus three. Now if you check that don&#x27;t mean here. Then we have three x plus five sort of a greater than zero. It means X would be greater than minus five. Divided by three and two x minus. Terry&#x27;s would be greater than zero. It implies that extra big, greater than three divided by two. So if we check that this prison, whether satisfied this or not, then the vigor the value of this is greater than three divided by two. It means this is the solution off this equation.

Amy Jiang · Answer

that&#x27;s so we have the fault in question and you&#x27;ll see that there&#x27;s addition between two natural log valleys on both the left hand side and the right hand side. So let&#x27;s use the product rule on both sides so he gets Ellen of X. Times X Plus five is equal to Owen of X plus one Times Experts Street. And now we could take both sides youto eat power, and that gives us this extend. Jax was five, so that&#x27;s X squared. Plus five X is equal to UM, that&#x27;s X plus one times X plus three. What is that equal to that? Gives me X squared Plus three acts plus X plus three. We have X squared plus four X plus three. You have X squared plus four x plus three. Okay, now we can subtract X squared on both sides. Thes Cancel. Now that&#x27;s subject for X on both sides. To get X is equal to three

Problem

Solve each equation for $x$ . $$(a)\ln (\ln x)…

Problem 49 Hard Difficulty

Solve each equation for $x$ .

$$(a)2^{x-5}=3 \quad \text { (b) } \ln x+\ln (x-1)=1$$

Answer

(a) $x=5+\log _{2} 3$
(b) $x=\frac{1+\sqrt{1+4 e}}{2} \approx 2.223$

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James Stewart

Biocalculus Calculus for the Life Sciences

Grace H.

Heather Z.

Kayleah T.

Kristen K.

Precalculus Review - Intro

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(a) $x=5+\log _{2} 3$(b) $x=\frac{1+\sqrt{1+4 e}}{2} \approx 2.223$

Biocalculus Calculus for the Life Sciences

Grace H.

Heather Z.

Kayleah T.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Heather Z.

Kayleah T.

Kristen K.

(a) $x=5+\log _{2} 3$
(b) $x=\frac{1+\sqrt{1+4 e}}{2} \approx 2.223$

James Stewart

Biocalculus Calculus for the Life Sciences